Independent families and asymptotic density

Abstract: Let $\mathcal{D}$ be the family of sets $S\subseteq \mathbb{N}$ for which the asymptotic density $$ d(S):=\lim_{n\to \infty}\frac{|S\cap [1,n]|}{n} $$ exists. Treating $d$ as a finitely additive probability measure on $\mathcal{D}$, we study structural properties of families of sets $\mathcal{A}\subseteq \mathcal{P}(\mathbb{N})$ which are independent (in its classical statistical meaning). We conclude with several open questions. Reference: J. Keith and P. Leonetti, On maximal families of independent sets with respect to asymptotic density , arxiv.org/abs/2603.28922.

number theory

Audience: researchers in the topic

( paper )

Combinatorial and additive number theory seminar (CANT 2026)